Arachne's sigil is weaving: threads appear and weave together the spell.
Gaius:
Laus:
Laus' sigil is related to pestilence: a foul odor and disgusting bugs appear when he casts his spells.
Lucius:
Lucius' casting sigil is based off the star trek transporter effect: bright blue sparkles. The sparkles tend to be orderly as opposed to haphazard.
Tomas:
Tomas' is very subtle. It's an unnoticable change in state. The idea is that you're never sure when exactly whatever happened happened.
Gaius:
Laus:
Lucius:
For the curious, or those with a high Hermetic Lore score, here are all of the sigils of the Lucius lineage.
Lucius the Elder Lucius the Younger Lucius III Lucius IV
Tomas:
Gaius:
Laus:
Lucius:
Lucius' handwriting style has the detail and neatness of this:
but with the slant of this:
Tomas: